Recall that the the vertical shifting of functions is associated with the numerical value that is added to the original one. A possitive value k will shift the function k units up, and a negativa value (or subtracting k) will move it vertically down k units.
If I understand correctly, you forgot to type an "x"in the original function f(x), which should read:
f(x) = 0.5 x
Correct?
The new graph is g(x) = 0.5 x - k which is obtained by shifting the original f(x) DOWN by 3 units.
In order to shift the graph of f(x) DOWN three units, we need to SUBTRACT 3 from f(x), leading to : 0.5 x - 3
Therefore, the value of "k"in the given g(x) = 0.5 x - k must be 3.
which agrees with the last option in your list (option D)
